I think the most realistic goal was always a main-frame type computer that could perform computations for special purposes. Not necessarily to shrink it down to phone-size or even a desktop. But maybe the marketing did really have this objective.
https://dyson-sphere-program.fandom.com/wiki/Quantum_Chip
QUANTUM CHIPS Running low? Never Again! | Dyson Sphere Program Master Class
Even worse, there is no reason to think that there will ever be - as far as we know, QCs only show an exponential advantage on problems with very very specific structures, while the whole problem of NP-hard problems is that they have no structure in general.
It is suspected to be NP but not even NP-complete, nevermind NP-hard. It is suspected not to be in P, but that is not yet proven.
Some problems in BQP are suspected to be in NP (integer factorization, for which the best known classical algorithm is sub-exponential, but we have a polynomial time quantum algorithm), but there is no known NP-complete problem for which a quantum algorithm is known, or even suspected to exist.
Edit - some links:
[0] https://www.scottaaronson.com/papers/npcomplete.pdf - chapter 4
> If we interpret the space of 2n possible assignments to a Boolean formula φ as a “database,” and the satisfying assignments of φ as “marked items,” then Bennett et al.’s result says that any quantum algorithm needs at least ∼n/2 steps to find a satisfying assignment of φ with high probability, unless the algorithm exploits the structure of φ in a nontrivial way. In other words, there is no “brute-force” quantum algorithm to solve NP-complete problems in polynomial time, just as there is no brute-force classical algorithm.
[1] https://youtu.be/0jrybODBUpA?t=30m28s "P versus NP"
First of all, while not proven, it is considered most likely that integer factorization is not in P, so potentially we already know of 1 NP-P problem which can have an exponential speed-up from a QC (Shor's algorithm).
Secondly, there is one non-exponential speedup that can potentially apply to even NP-complete problems - using Grover's algorithm to find an element in an unordered list with complexity O(sqrt(n)) instead of the classical O(n).
Ironically, if that were to happen, it would probably be a much more important boon for humanity than if we successfully build a working QC.
It could very well be that they are both great approximations and it’s actually the underlying information structure that shifts depending on scale. This doesn’t seem likely to us perhaps, but only because of existing intuition which we know is likely wrong at some level.
> It could very well be that they are both great approximations and it’s actually the underlying information structure that shifts depending on scale.
Right now, both QM and GR claim that they apply at any scale. If it turns out that the laws of physics change with scale, that means that both QM and GR are wrong, even though they may each be perfectly correct at the scale they have been seen to work so far.
the thing is I don't believe that either does make such a claim. I believe certain people have said that and the untrained masses may assume that's the case. But I don't think the scholarly proponents or intellectual founders of either system made such a claim (in fact Newton was religious and Einstein believed we were way off by his death.)
>that means that both QM and GR are wrong
How though? They are both right for their use case so are likely subsets of a greater theory.
Not only does the math apply at any scale, but no one has any idea how to add a scale parameter to prevent it from doing so, or what value that parameter should have. QM at least has the Measurement Postulate that could allow this to fit, but no scale is added.
Note that when I say "a scale parameter", I'm referring to something like the sqrt(1-v²/c²) of special relativity, but for "size", added to the Schrodinger equation and to Einstein's equations, that would mean they take the "scale" of the phenomenon into account. Without such a parameter, the equation says that it applies to a star as well as to a neutron. The only reason we don't apply them that way is that we have already tried and we know they give the wrong results.
Also, both GR and QM give the right results if applied at the scales of day to day life. You can use the Schrodinger equation and the Born postulate to compute where two trains traveling in opposite direction with some speed will meet, or you can use Einstein's field equations, and you'll get the same response within some small margin or error (with some reasonable assumptions, such as an almost flat spacetime in the area).
Furthermore, there are at least significant numbers of QM practitioners who do believe that QM applies at any scale - those who believe in the Many Worlds Interpretation, which states this very explicitly. On the GR side, the limitations of GR if applied at subatomic scales are well accepted and considered a flaw in the theory - which is why people hope to replace it with a theory of quantum gravity.
And Shor is based on quantum superior FFT if I recall correctly, which could have applications outside of discrete log.
Disclaimer: I’m not an expert on this stuff, I’m sure someone will correct me if I’m wrong because there are real pros on here.